Minimal sets in monotone and sublinear skew-product semiflows I: the general case,
with Rafael Obaya and Ana M. Sanz,
J. Differential Equations 247 (7) (2010), 1879-1897.
The dynamics of a general monotone and sublinear skew-product semiflow
is analyzed, paying special attention to the long-term behavior of the
strongly positive semiorbits and to the minimal sets. Four possibilities
arise depending on the existence or absence of strongly positive minimal sets
and bounded semiorbits, as well as on the coexistence or not of bounded and unbounded
strongly positive semiorbits. Previous results are unified and extended,
and scenarios which are impossible in the autonomous or periodic cases are described.